Question: Which of the following numbers is a factor of 144? ${5,7,9,13,14}$
Answer: By definition, a factor of a number will divide evenly into that number. We can start by dividing $144$ by each of our answer choices. $144 \div 5 = 28\text{ R }4$ $144 \div 7 = 20\text{ R }4$ $144 \div 9 = 16$ $144 \div 13 = 11\text{ R }1$ $144 \div 14 = 10\text{ R }4$ The only answer choice that divides into $144$ with no remainder is $9$ $ 16$ $9$ $144$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $9$ are contained within the prime factors of $144$ $144 = 2\times2\times2\times2\times3\times3 9 = 3\times3$ Therefore the only factor of $144$ out of our choices is $9$. We can say that $144$ is divisible by $9$.